GMAT Math : Calculating the area of a square

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Example Question #11 : Calculating The Area Of A Square

Squares

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square  and Square . The ratio of  to  is 13 to 2. What is the ratio of the area of Square  to that of Square ?

Possible Answers:

Correct answer:

Explanation:

To make this easier, assume that  and  - the reasoning generalizes. Then Square  has sidelength 15 and area . The sidelength of Square , each side being a hypotenuse of a right triangle with legs 2 and 13, is 

.

The square of this, 173, is the area of Square .

The ratio is .

Example Question #12 : Calculating The Area Of A Square

Squares

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square  and Square .  The ratio of  to  is 7 to 1.

Which of these responses comes closest to what percent the area of Square  is of that of Square ?

 

Possible Answers:

Correct answer:

Explanation:

To make this easier, assume that  and ; the results generalize. 

Each side of Square  has length 8, so the area of Square  is 64. 

Each of the four right triangles has legs 7 and 1, so each has area ; Square  has area four times this subtracted from the area of Square , or

.

The area of Square  is

of that of Square .

Of the five choices, 80% comes closest.

Example Question #13 : Calculating The Area Of A Square

The perimeter of a square is the same as the circumference of a circle with area 100. What is the area of the square?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a circle is

.

If the area is 100, the radius is as follows:

The circle has circumference  times its radius, or

This is also the perimeter of the square, so the sidelength of the square is one-fourth this, or

The area of the square is the square of this, or 

Example Question #14 : Calculating The Area Of A Square

The perimeter of a square is the same as the circumference of a circle with radius 8. What is the area of the square?

Possible Answers:

The correct answer is not among the other choices.

Correct answer:

Explanation:

A circle with radius 8 has as its circumference  times this, or 

.

This is also the perimeter of the square, so the sidelength is one fourth of this, or 

.

The area is the square of this, or

.

Example Question #171 : Geometry

The perimeter of a square is the same as the length of the hypotenuse of a right triangle with legs 8 and 12. What is the area of the square?

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

Explanation:

The length of the hypotenuse of a right triangle with legs 8 and 12 can be determined using the Pythagorean Theorem:

Since this is also the perimeter of the square, its sidelength is one fourth of this, or

The area of the square is the square of this sidelength, or 

Example Question #11 : Calculating The Area Of A Square

If the perimeter of a square is , what is its area?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a square, and any shape for that matter, is found by adding up all the exterior sides. Since all sides are equal in a square, we can say: 

where  represents the length of a side

We can solve for the side length using the information provided:

The area of a square is found by squaring the side length: 

Example Question #61 : Quadrilaterals

The perimeter of a square is . Give its area.

Possible Answers:

Correct answer:

Explanation:

The length of one side of a square is the perimeter divided by 4:

Square this to get the area:

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